Abstract: The area of inverse problems can be thought of as the Jeopardy! of mathematical research. Instead of trying to find solutions to complicated equations, the theory of inverse problems attempts to do the opposite: Given solutions to equations, what are the equations themselves? Just as many questions have the same answer, it is true that many different equations have the same solution, making inverse problems extremely challenging to solve. In this talk I’ll describe the inverse problem of sampling continuous signals, and how to guarantee a perfect reconstruction by preventing the occurrence of “alias” signals.